Conduction

Pagina 1

1 HEAT TRANSFER & THERMAL ANALYSIS CONDUCTION-1 Problem 1 A section of a composite wall with the dimensions shown below has uniform temperatures of 200 °C and 50 °C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA = 70 W/(m K), kB = 60 W/(m K), kc = 40 W/(m K) and kD = 20 W/(m K), determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces. Calculate also the amount of thermal power crossing wall B. Solution The thermal circuit for the composite wall is shown below ©2 0 1 1C e n g a g eL e a r n i n g .A l lR i g h t sR e s e r v e d .M a yn o tb es c a n n e d ,c o p i e do rd u p l i c a t e d ,o rp o s t e dt oap u b l i c l ya c c e s s i b l ew e b s i t e ,i nw h o l eo ri np a r t . 37 PROBLEM 1.31 As e c t i o no fac o m p o s i t ew a l lw i t ht h ed i m e n s i o n ss h o w nb e l o wh a su n i f o r m temperatures of 200°C and 50°C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA =7 0W / ( mK ) , kB =6 0W / ( mK ) , kc =4 0W / ( mK )a n dkD =2 0W / ( mK ) ,d e t e r m i n et h er a t eo fh e a tt r a n s f e rt h r o u g ht h i s section of the wall and the temperatures at the interfaces. GIVEN x As e c t i o no fac o m p o s i t ew a l l x Thermal conductivities ƒ kA =7 0W / ( mK ) ƒ kB =6 0W / ( mK ) ƒ kC =4 0W / ( mK ) ƒ kD =2 0W / ( mK ) x Surface temperatures ƒ Left side (TAs) = 200°C ƒ Right side (TDs) = 50°C FIND (a) Rate of heat transfer through the wall ( q) (b) Temperature at the interfaces ASSUMPTIONS x One dimensional conduction x The system is in steady state x The contact resistances between the materials is negligible SKETCH SOLUTION The thermal circuit for the composite wall is…